BOSTON — As a boy, J. William Fulbright never imagined that he would become a conspicuous voice in America's relations with the world.

Grain -- not missile -- silos bounded the world of his father's Arkansas farm. Exotic places had names like Kansas City.

''I never went to an opera, or even to a large city, until I got the Rhodes scholarship and went to Oxford,'' the 81-year-old former U.S. senator, statesman and frequent critic of the presidency said during a recent visit here.

''Well, I had been to the great amusement park at Kansas City -- it was all electrical -- but that was about it. That changed quick when I got to England. It was quite a culture shock.''

Almost 60 years later, Fulbright could look back on his career, if he chose to, with pride. The chairman of the Senate's Foreign Relations Committee from 1958 to 1974, he exerted key influence on conduct of the Vietnam War when he challenged President Lyndon B. Johnson and the ''secret war'' the White House was waging in Southeast Asia. Fulbright's criticism helped turned public opinion against the war.

Instead of merely looking back, however, Fulbright looks around and ahead, with sadness and anger.

He is saddened by the country's ''obsessive'' mistrust of the Soviet Union, which, he says, ''lies at the heart'' of the nuclear arms race. ''The problem isn't one of too many weapons, but of too little trust,'' he said.

Fulbright is also nettled by the White House's Iran initiative, which he calls ''a terrible abuse of power.''

Finally, there are personal woes and aches -- of aging, of diminishing eyesight, the death last year of Betty, his wife.

Yet Fulbright still finds ground for hope in the scholarship program that bears his name.

Forty years ago he wrote the bill that led to the Educational Exchange Program, the largest exchange of scholars in history. More than 156,000 scholars from 100 countries have participated. One third have been Americans sent abroad for graduate study, research or teaching; the rest have come to the United States.

Today, as he travels the country marking the 40th anniversary of the program, Fulbright's eyes brighten as he discusses his private hope for the program: to promote understanding between people of the United States and those in foreign lands.

''It's a chance to get at the heart of the nuclear problem,'' Fulbright said at Harvard University. ''And the whole cost of the program since it started wouldn't buy half a submarine.''

''Constantly you hear Soviet leader Mikhail Gorbachev or President Reagan say that they don't make agreements because they don't trust each other. If that's the problem, diddling around with a few thousand weapons isn't going to make much difference because we have so much overkill.''

''What do you do about it? An exchange of some of the best young scholars can lay the groundwork for creating more trust and understanding. Any joint venture you do with an adversary builds trust. It isn't that you're going to suddenly love your enemy, but you understand him, his culture, his intentions. You come to see that he isn't anxious to do you in at the first opportunity.'' Since losing his Senate seat to Dale Bumpers in 1974 and joining a Washington law firm, Fulbright has mused much on what he calls the psychology of American foreign policy and the enormous growth of presidential power.

Fulbright furrowed his brow as he thought about negative U.S. attitudes toward the Soviets.

''It doesn't make any sense. We've never been at war with the Soviet Union, if you don't count the troops we sent in after their revolution. They never attacked us either. The British burned down the White House, but there's nobody else we love more than the British. The problem is that if you hear again and again that the Russians are monsters, sooner or later you believe it, and that expectation affects our foreign policy.''